Thermodynamics

82 | Thermodynamics38%73%Gas RangeElectric RangeEXAMPLE 2–15Cost of Cooking with Electric and Gas RangesThe efficiency of cooking appliances affects the internal heat gain from themsince an inefficient appliance consumes a greater amount of energy for thesame task, and the excess energy consumed shows up as heat in the livingspace. The efficiency of open burners is determined to be 73 percent forelectric units and 38 percent for gas units (Fig. 2–57). Consider a 2-kWelectric burner at a location where the unit costs of electricity and naturalgas are $0.09/kWh and $0.55/therm, respectively. Determine the rate ofenergy consumption by the burner and the unit cost of utilized energy forboth electric and gas burners.FIGURE 2–57Schematic of the 73 percent efficientelectric heating unit and 38 percentefficient gas burner discussed inExample 2–15.Solution The operation of electric and gas ranges is considered. The rate ofenergy consumption and the unit cost of utilized energy are to be determined.Analysis The efficiency of the electric heater is given to be 73 percent.Therefore, a burner that consumes 2 kW of electrical energy will supplyQ # utilized 1Energy input2 1Efficiency2 12 kW2 10.732 1.46 kWof useful energy. The unit cost of utilized energy is inversely proportional tothe efficiency, and is determined fromCost of energy inputCost of utilized energy EfficiencyNoting that the efficiency of a gas burner is 38 percent, the energy inputto a gas burner that supplies utilized energy at the same rate (1.46 kW) isQ # input, gas Q# utilized 1.46 kW 3.84 kW1 13,100 Btu>h2Efficiency 0.38since 1 kW 3412 Btu/h. Therefore, a gas burner should have a rating of atleast 13,100 Btu/h to perform as well as the electric unit.Noting that 1 therm 29.3 kWh, the unit cost of utilized energy in thecase of a gas burner is determined to beCost of energy input $0.55>29.3 kWhCost of utilized energy Efficiency0.38 $0.049>kWh $0.09>kWh0.73 $0.123>kWhDiscussion The cost of utilized gas is less than half of the unit cost of utilizedelectricity. Therefore, despite its higher efficiency, cooking with anelectric burner will cost more than twice as much compared to a gas burnerin this case. This explains why cost-conscious consumers always ask for gasappliances, and it is not wise to use electricity for heating purposes.Efficiencies of Mechanical and Electrical DevicesThe transfer of mechanical energy is usually accomplished by a rotatingshaft, and thus mechanical work is often referred to as shaft work. A pumpor a fan receives shaft work (usually from an electric motor) and transfers itto the fluid as mechanical energy (less frictional losses). A turbine, on theother hand, converts the mechanical energy of a fluid to shaft work. In theabsence of any irreversibilities such as friction, mechanical energy can be